Stable discrete soliton molecules in two-dimensional waveguide arrays

We consider a bound state of two discrete solitons in a two-dimensional waveguide array. Using numerical and variational calculations, we investigate the effect of binding on the mobility of the two solitons, which we found to be marginal. Considering anisotropic waveguides, where coupling in one direction is stronger than in the other, we show that mobility is enhanced considerably along the weaker-coupling direction. We show also that a stable bound state of two solitons exists in such a setup where each one of the two solitons is located at a different waveguide. The stability of the resulting soliton molecule is provided by the Peierls-Nabarro potential and the mobility of the individual solitons is facilitated by the anisotropy. Considering a combination of two out-of-phase solitons, we find that they form a metastable state of a single soliton that suddenly splits into two solitons propagating away from each other.